The side lengths 9, 13, and 17 form a triangle.


TrueFalse

Answer:

363.741 feet

Step-by-step explanation:

Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;

Tan θ = \(\frac{opposite side}{adjacent side}\)

Tan \(60^{0}\) = \(\frac{x}{210}\)

cross multiply to have;

   x = 210 × Tan \(60^{0}\)

      = 210 × 1.7321

      = 363.741

The cliff is 363.741 feet high.

The two consecutive integers that the square root of 12 lies between are 3 and 4.

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. This therefore means that integers can only be whole numbers and consecutive integers follow each other. For instance, 1, 2, and 3 are consecutive integers.

To find the two consecutive integers that the square root of 12 lies between, find the square root of 12 :

= √ 12

= 3.46

This means that the lower integer would be 3 and the consecutive integer following would be 4.

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Answer:

Train A is 287 tons

Train B is 94 tons

Step-by-step explanation:

My method of solving it may have been a bit different from how you were taught. I divided 381 by 2 to give both trains an equal weight of 190.5 tons. I then divided the difference, 193, by 2 to get 96.5 tons. I subtracted the new difference from the weight of Train B and added it to train A. To double check, you can grab a calculator and see that their weights are equal to 381.

In the given production function Y = F(K,L) = [aK^μ + bL^μ]^1/μ, where μ < 0, several calculations and conclusions are made. First, it is shown that as k approaches 0, the limit of ak^μ + b is b. This result is used to demonstrate that F(0, L) equals 0. Among the three Inada conditions, the condition F_k(0, L) = ∞ does not hold in this case. In terms of the capital income share in GDP, it is shown that s_K = YrK = (a + bk^(-μ))/a. The variation of s_K with k depends on the sign of μ, and when μ is very close to zero, s_K tends to approach infinity. The marginal product of labor is computed and expressed as a function of k, which leads to the conclusion that k = (b/a)^(1/(1-μ))r/w. Finally, it is concluded that the elasticity of substitution between labor and capital is constant and equal to 1-μ.

In part (f), the limit of ak^μ + b as k approaches 0 is computed. Since μ < 0, the term ak^μ approaches 0, and the limit simplifies to b. This result is then used in showing that F(0, L) equals 0, as the term [aK^μ + bL^μ]^1/μ reduces to [bL^μ]^1/μ = bL.

Moving on to part (g), the capital income share in GDP, denoted as s_K, is derived as YrK = (a + bk^(-μ))/a. The variation of s_K with k depends on the sign of μ. If μ is negative, s_K decreases as k increases, indicating a declining capital income share. However, if μ is very close to zero, s_K tends to approach infinity, implying a dominant capital income share.

In part (h), the marginal product of labor is computed and expressed as a function of k. Utilizing the result from part (c), it is concluded that k = (b/a)^(1/(1-μ))r/w, where r denotes the rental rate of capital and w represents the wage rate.

Finally, in part (i), it is concluded that the elasticity of substitution between labor and capital is constant and equal to 1-μ. This implies that the relative responsiveness of the factor inputs, labor and capital, remains consistent and depends on the value of μ.

Overall, these calculations and conclusions provide insights into the behavior and relationships within the given production function.

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Answer:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

Step-by-step explanation:

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer:

x = 6

Step-by-step explanation:

CT is a median, which means it divided AB into two equal parts so we can write the following equation:

7x + 9 = 5x + 21 transfer like terms to the same side of the equation

7x - 5x = 21 - 9 do the extraction

2x = 12 divide both sides by 2

x = 6

The total proportion of shirts between two prices is 0.9431, which is obtained using the knowledge of proportion and statistics.

What is proportion?

In mathematics, a proportion is defined as the comparison between two numerical quantities. If both possess the same nature, they are called directly proportional, or else called inversely proportional.

Calculation of the proportion based on the problem

The mean and standard deviation are given to be 45 and 5 respectively

Calculate standard normal variate using the formula, z = (x - 45) / 5

Taking x = 37, we get,

z1 = (37 - 45) / 5

= -1.6

Using the z table, we get the value, z1 = 0.0548

Now, taking x = 59.35, we get,

z2 = (59.35 - 45) / 5

= 2.87

Using the z table, we get the value, z2 = 0.9979

The proportion between two prices is given by z = z2 - z1

z = 0.9979 - 0.0548

= 0.9431

Hence, the proportion of shirts between the two prices is 0.9431.

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The time at which the pool was full is 4:00 when the water is in the 4 inches tank .

In mathematics, multiplication is one of the four basic arithmetic operations. It represents the basic idea of repeated addition of the same number.

The height of the tank is 4 feet water pouring is turned on at 11:00 at 11:25 the depth of the water in the tank is 4 inches.

which means,

To fill 4 inches it takes = 25 min

To fill 1 inch it takes = 25/4 min 4 feet = 4×2.54 = 48 inches

To fill 48 inches it takes = 48 × 25/4

                     = 300 min

                          = 5 hours

So, 5 hours after 11:00 will be 4:00

Hence, the time at which the pool was full is 4:00

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The elements of Z3[x]/(x^2 - x) are of the form ax + b that is multiplication table, where a and b are elements of Z3.

The multiplication table is:

  | 0   1   x   1+x   2   2+x

-------------------------------

0 | 0   0   0    0   0   0

1 | 0   1   x   1+x  2  2+x

x | 0   x  2x  2+x   x  1+2x

1+x| 0  1+x 2+x   2  2+x  x

2 | 0   2   x   2+x  1  1+x

2+x| 0  2+x 1+2x  x  1+x 2

Note that in this table, we use the fact that x^2 - x = 0, which implies that x^2 = x.

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Answer:

y=-9/8x+7

Step-by-step explanation:

When finding slope from the graph, the coordinate that has a zero where x is supposed to be is the y-intercept. To put it into slope-intercept form it is important to remember y=mx+b. B is the y-intercept so you'll take the y value and put it where b is. So in this case you'll have y=mx+7. To find the slope you have to find the distance between the two coordinates. So you'll see how many times you go up from -2 to 7, 9 times. Then you calculate how many times you go over from 8 to 0, 8 times. The 8 and the 9 are the two values of slope. When forming the slope you put the rise over the run. Or in other words, you put how many times you go up/down over how many times you go left/right. To determine if the slope is negative or positive you look at the line and if the values are getting smaller or the line is going from left to right, then it is negative. If the values are getting bigger or the line is going from right to left, then it is positive. In this case the values are getting smaller and the line is going from left to right which means this slope is negative. So you add a negative to 9/8 and replace m with what you just got (the slope). Your answer should look like this, y=-9/8x+7.

The option that Sarah should choose is option 2.

Sarah would choose the option that give her the higher amount of money at her 21st birthday.

The amount that Sarah would earn each year with option 1 would increase at a linear rate. This is because she gets the same amount of money each year.

The form of a linear equation is y = mx + b

Where:

The amount that Sarah would earn each year with option 2 would increase at an exponential rate.

The general form of exponential equation is f(x) = \(e^{x}\)

Where:

The rate of growth with an exponential function is faster than that of a linear function. It is for this reason that option 2 is the better option.

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The solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

According to the given question.

We have a linear equation in one variable.

4y - 6 = 2y + 8

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is given by

4y - 6 = 2y + 8

⇒ 4y - 2y - 6 = 8     ( subtracting 2y from both the sides)

⇒ 2y -6 -8 = 0           (subtracting 8 from both the sides)

⇒ 2y - 14 = 0

⇒ 2y = 14

⇒ y = 14/2

⇒ y = 7

Hence, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

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Answer:

3%=0.03 3%1÷2 =0.015. ..........,...

\(3 \frac{1}{4} - 4 \frac{1}{2} \\ \\ \longrightarrow \: \frac{13}{4} - \frac{9}{2} \\ \\ taking \: LCM \\ \\ \longrightarrow \: \frac{13 - 18}{4} \\ \\ \longrightarrow \: \boxed{ \frac{ - 5}{4} }\)

hope helpful! :-;

In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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Answer:

1024

Step-by-step explanation:

We can solve this using areas.

The small triangle has a base b and a height h.

The area of the small triangle is bh/2.

The large triangle has a perimeter that is 32 times the perimeter of the small triangle. Perimeters are linear measures, so the linear scale factor from the small triangle to the large triangle is 1:32. That means that the base of the large triangle measures 32b, and the height of the large triangle measures 32h.

The area of the large triangle is

base × height / 2 = (32b)(32h)/2 = 512bh

Now we compare the areas of the the large triangle and the small triangle by division.

512bh / (bh/2) = 512 × 2 = 1024

Answer: 1024

Answer:

50000

Step-by-step explanation:

Using

\(P(percentage) \times CP(cost \: price) = Sales \: Tax\)

Putting the given values

P × 25000 = 1750

\(P = \frac{1750}{25000} \)

\(P = 0.07 \times 100\)

\(P = 7\%\)

Now

For purchase price of a new car.

\(P \times CP=Sales \: Tax\)

\(7 \times CP = 3500\)

\(CP = 50000\)

Hope it helps you, any confusions you may ask!

The height of the shadow (s) as a function of the distance (d) from the man to the building is:

s = 0.21 d

Given that a spotlight is 10 m away from a building and a man 2.1 m tall crosses it,

We need to write the height of the shadow (s) as a function of the distance (d) from the man to the building.

To determine the height of the shadow (s) as a function of the distance (d) from the man to the building, we can make use of similar triangles.

We can observe that the man, the top of the shadow, and the top of the building form similar triangles. The ratio of the corresponding sides of similar triangles is equal, so we can write:

s / d = man_height / distance_to_building

Substituting the given values into the equation:

s / d = 2.1 / 10

To isolate s, we can cross-multiply:

s = (2.1 / 10) x d

Therefore, the height of the shadow (s) as a function of the distance (d) from the man to the building is:

s = 0.21 d

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The system of linear equation for the graph are: y = -1/3x + 3 and y = 3x - 7.

A system of linear equation is a combination of two linear equation. Each linear equation is made of algebraic equation that consists of variables, constant, and arithmetic operation.

To determine the linear equation on the graph, we need to find two points on the each line on the graph and determine the slope-intercept form.

For the first decreasing line to the left, we have the two points

(0, 3)(9,0)

Using the slope intercept form y = mx + b. The linear equation for the first line is: y = -1/3x + 3

For the second increasing line to the right, the two points are:

(3,2)(0,-7)

The linear equation for the second line is:

y = 3x - 7

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Answer: -1

Step-by-step explanation: A typical quadratic equation is \(ax^{2} +bx+c\) and the maximum value formula is -b/2a, so let plug it in -4/2(-4) which equals 1/2. Then let plug 1/2 into the equation,

-4(1/2)^2+4(1/2)-2=

    -1+2-2=

          -1

Answer:

you have to isolate the variable

Step-by-step explanation:

7k-14=42

+14    +14

7k=56

7k/7+56/7

k=8

: )

7+(-1) = -3

Steps of adding 7+(-10) using number line are as following:

1) Draw a number line by ranging from -10 to +10.

2) Point out 7 on the number line.

3) Because -10 is added to 7 on the number line, please move 10 numbers left to 7 on the number line. We always go left in addition of a negative number on the number line.

4) The number we reach -3 on left side would be our final sum.

5) From the number we can clearly see that moving 10 number on left to 7, we get -3.

Note: We are moving left because of negative sign in front of 10.

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Answer:

Keith; -5, -12

Step-by-step explanation:

Logic ( Subtract 12 from both sides, then factor it out)

Answer:

Opposite of 7= -7

Step-by-step explanation:

A, C, and E are linear transformations.  To justify:  A: T(A) = ASA-I is linear because it satisfies the two properties of linearity:

1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.

C: T(A) = A from R to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R. This can be shown by plugging in kA for A in T(A) and simplifying.

E: T(A) = A from R2x2 to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.

B, D, and J are not linear transformations.

To justify:

B: T(A) = A from R2xs to R2x5 is not linear because it does not satisfy the additivity property of linearity. Specifically, T(A+B) ≠ T(A) + T(B) for some matrices A and B in R2xs.

D: T(A) = 2A from R6x4 to R6x4 is not linear because it does not satisfy the homogeneity property of linearity. Specifically, T(kA) ≠ kT(A) for some scalar k and matrix A in R6x4.

J: T(A) = A+Is from RSx5 to RSx5 is not linear because it does not satisfy either the additivity or homogeneity properties of linearity. Specifically, T(A+B) ≠ T(A) + T(B) and T(kA) ≠ kT(A) for some matrices A and B in RSx5 and scalar k.

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Therefore, the standard form of the equation for the given circle is:

49x^2 + 64y^2 - 28xy + 48x - 72y - 527 = 0

To find the standard form of the equation for a circle given its center and radius, we use the formula:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the coordinates of the center of the circle, and r represents the radius.

In this case, the center of the circle is given as ((7)/(8), (-3)/(7)), and the radius is 3.

Substituting these values into the formula, we get:

(x - (7)/(8))^2 + (y - (-3)/(7))^2 = 3^2

Simplifying further, we have:

(x - (7)/(8))^2 + (y + (3)/(7))^2 = 9

Now, we can expand the equation and put it in standard form:

(x^2 - (7)/(4)x + (49)/(64)) + (y^2 + (6)/(7)y + (9)/(49)) = 9

Combining like terms, we have:

x^2 + y^2 - (7)/(4)x + (6)/(7)y + (49)/(64) + (9)/(49) = 9

Multiplying through by the denominators to clear the fractions, we obtain:

49x^2 + 64y^2 - 28xy + 48x - 72y + 49 = 576

Rearranging the terms, we get:

49x^2 + 64y^2 - 28xy + 48x - 72y - 527 = 0

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Answer:

Step-by-step explanation:

For question 1:The answer is 36-k.

Question 2: The answer is 61.

Question 3: The answer is 162.